From First Corinthians by George T. Montague, SM, commenting on First Corinthians 5:6b-8

Yeast makes bread to rise, but it also corrupts. . . . A little yeast leavens all the dough. (The saying is repeated in Gal 5:9.) Indeed, it takes very little compared to the rest of the flour. Paul’s point is that one tolerated scandal can spoil the whole community, both within and as seen by outsiders.

The only way to assure that there is no corruption is to become a fresh batch of dough: to start over. But lest they misinterpret that, Paul qualifies the metaphor by telling the community, You are unleavened. The community does not need to be founded all over again. Their commitment to Christ and their baptismal consecration have made them a holy people, a people already set aside for God. They must therefore become what they are. Eliminating the corrupting influence is the only way to maintain the integrity of their consecration. The reason they are unleavened is that the true paschal lamb, Christ, has been sacrificed. At Passover the lambs were sacrificed, and Paul here represents the earliest New Testament claim that in his death and resurrection, Christ is the fulfillment of the Jewish Passover. There is a clear causal connection between their being unleavened and the sacrifice of Jesus, as the connective for indicates. The sacrificing of the lambs in the temple only signaled the time for the Jews to clean out all leaven from their homes; the slaughtered lamb did not cleanse the leaven. But the sacrifice of Jesus the Lamb cast out the leaven and made “a new creation” (2 Cor 5:17), a completely new dough. That is what the Christian community is.

Christians’ Passover week never ends, and that is why there should never be a corrupting influence in their midst at all. Thus they celebrate the feast constantly and should live accordingly, with sincerity and truth. This phrase targets the Corinthians’ sweeping under the rug the corrupting influence of sin in their midst.